Mixed-integer linear approximations of AC power flow equations for systems under abnormal operating conditions

We present a methodology to generate mixed-integer linear approximations of the AC power flow equations governing lines, transformers (including tap regulators and phase shifters), shunt and series compensators, and consumption responsive to voltage. Our motivation is to employ these models in grid topology optimization of realistic power grids under abnormal or uncommon operating conditions, where usual assumptions for relaxing the power flow equations may not hold. The method constructs piecewise linear approximations of the non-linear power flow equations by minimizing the squared approximation error over a subset of the feasible domain. We test the method using a realistic database for the Chilean system (1548 buses, 1114 lines, 564 transformers). The resulting approximations yield root mean square errors in the order of 0.05pu and are successfully applied to solve a transmission switching instance for the system.